Data-driven model discovery of ideal four-wave mixing in nonlinear fibre optics

Andrei V. Ermolaev; Anastasiia Sheveleva; Goëry Genty; Christophe Finot; John M. Dudley

doi:10.1038/s41598-022-16586-5

Data-driven model discovery of ideal four-wave mixing in nonlinear fibre optics

Andrei V. Ermolaev, Anastasiia Sheveleva, Goëry Genty, Christophe Finot, John M. Dudley

Physics

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Abstract

We show using numerical simulations that data driven discovery using sparse regression can be used to extract the governing differential equation model of ideal four-wave mixing in a nonlinear Schrödinger equation optical fibre system. Specifically, we consider the evolution of a strong single frequency pump interacting with two frequency detuned sidebands where the dynamics are governed by a reduced Hamiltonian system describing pump-sideband coupling. Based only on generated dynamical data from this system, sparse regression successfully recovers the underlying physical model, fully capturing the dynamical landscape on both sides of the system separatrix. We also discuss how analysing an ensemble over different initial conditions allows us to reliably identify the governing model in the presence of noise. These results extend the use of data driven discovery to ideal four-wave mixing in nonlinear Schrödinger equation systems.

Original language	English
Article number	12711
Number of pages	11
Journal	Scientific Reports
Volume	12
Issue number	1
DOIs	https://doi.org/10.1038/s41598-022-16586-5
Publication status	Published - 26 Jul 2022
Publication type	A1 Journal article-refereed

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title = "Data-driven model discovery of ideal four-wave mixing in nonlinear fibre optics",

abstract = "We show using numerical simulations that data driven discovery using sparse regression can be used to extract the governing differential equation model of ideal four-wave mixing in a nonlinear Schr{\"o}dinger equation optical fibre system. Specifically, we consider the evolution of a strong single frequency pump interacting with two frequency detuned sidebands where the dynamics are governed by a reduced Hamiltonian system describing pump-sideband coupling. Based only on generated dynamical data from this system, sparse regression successfully recovers the underlying physical model, fully capturing the dynamical landscape on both sides of the system separatrix. We also discuss how analysing an ensemble over different initial conditions allows us to reliably identify the governing model in the presence of noise. These results extend the use of data driven discovery to ideal four-wave mixing in nonlinear Schr{\"o}dinger equation systems.",

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AU - Finot, Christophe

AU - Dudley, John M.

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N2 - We show using numerical simulations that data driven discovery using sparse regression can be used to extract the governing differential equation model of ideal four-wave mixing in a nonlinear Schrödinger equation optical fibre system. Specifically, we consider the evolution of a strong single frequency pump interacting with two frequency detuned sidebands where the dynamics are governed by a reduced Hamiltonian system describing pump-sideband coupling. Based only on generated dynamical data from this system, sparse regression successfully recovers the underlying physical model, fully capturing the dynamical landscape on both sides of the system separatrix. We also discuss how analysing an ensemble over different initial conditions allows us to reliably identify the governing model in the presence of noise. These results extend the use of data driven discovery to ideal four-wave mixing in nonlinear Schrödinger equation systems.

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Data-driven model discovery of ideal four-wave mixing in nonlinear fibre optics

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